ç©åˆ†æ³• - Wikipedia
関数ã®å®šç©åˆ†ã¯ã€ãã®ã‚°ãƒ©ãƒ•ã«ã‚ˆã£ã¦å›²ã¾ã‚Œã‚‹é ˜åŸŸã®ç¬¦å·ä»˜é¢ç©ã¨ã—ã¦è¡¨ã™ã“ã¨ãŒã§ãる。 ç©åˆ†ã¨ã¯ä½•ã‹?（アニメーション） ç©åˆ†æ³•ï¼ˆã›ãã¶ã‚“ã»ã†ã€è‹±: integral calculus）ã¯ã€å¾®åˆ†æ³•ã¨ã¨ã‚‚ã«å¾®åˆ†ç©åˆ†å¦ã§å¯¾ã‚’ãªã™ä¸»è¦ãªåˆ†é‡Žã§ã‚る。 説明ã§ã®æ•°å¼ã®æ›¸ãæ–¹ã¯åºƒãæ™®åŠã—ã¦ã„るライプニッツã®è¨˜æ³•ã«æº–ãšã‚‹ã€‚ 実数直線上ã®åŒºé–“ [a, b] 上ã§å®šç¾©ã•ã‚Œã‚‹å®Ÿå¤‰æ•° x ã®é–¢æ•° f ã®å®šç©åˆ†ï¼ˆç‹¬: bestimmtes Integralã€è‹±: definite integralã€ä»: intégrale définie） ã¯ã€ç•¥å¼çš„ã«è¨€ãˆã° f ã®ã‚°ãƒ©ãƒ•ã¨ x 軸ã€ãŠã‚ˆã³ x = a 㨠x = b ã§å›²ã¾ã‚Œã‚‹ xy å¹³é¢ã®é ˜åŸŸã®ç¬¦å·ä»˜é¢ç©ã¨ã—ã¦å®šç¾©ã•ã‚Œã‚‹ã€‚ 「ç©åˆ†ã€ï¼ˆintegral）ã¨ã„ã†è¡“語ã¯ã€åŽŸå§‹é–¢æ•°ã™ãªã‚ã¡ã€å¾®åˆ†ã—ã¦ä¸Žãˆã‚‰ã‚ŒãŸé–¢æ•° f ã¨ãªã‚‹ã‚ˆã†ãªåˆ¥ã®é–¢æ•° F ã®æ¦‚念を指ã™ã“ã¨ã‚‚ã‚ã‚Šã€ã
ルベーグç©åˆ† - Wikipedia
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Riemann–Stieltjes integral - Wikipedia
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first published in 1894 by Stieltjes.[1] It serves as an instructive and useful precursor of the Lebesgue integral, and an invaluable tool in unifying equivalent forms of statistical theorems that apply to discret
Random variable - Wikipedia
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.[1] The term 'random variable' in its mathematical definition refers to neither randomness nor variability[2] but instead is a mathematical function in which the domain is the set of possible outcomes in a sample space (e.
Stochastic process - Wikipedia
A computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.[1][2][3] In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables in a probability sp
Probability space - Wikipedia
In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements:[1][2] A sample space, , which is the set of all possible outcomes. An event space, which is a set of events
Probability axioms - Wikipedia
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933.[1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases.[2] There are several other (equivalent) approaches to formalising probability. Bayesians will often motivate the Kolmogorov axiom
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Measure (mathematics) - Wikipedia
This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (January 2021) (Learn how and when to remove this message) Informally, a measure has the property of being monotone in the sense that if is a subset of the measure of is less than or equal to the measure of Furthermor
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Matlab programs for SDE
Diffusion process - Wikipedia
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